Question : If $\cos x=\sin y$ and $\cot(x–40°)=\tan(50°–y)$, then the values of $x$ and $y$ are:

Question : If $\cos\left(40^\circ+x\right)=\sin 30^\circ$, then the value of $x$ is:

Question : If $\sin Y=x$, then what will be the value of $\cos 2Y\left(\right.$ where $\left.0 \leq Y \leq 90^{\circ}\right)$?

Question : What will be the value of $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$?

Question : If $x\sin^{3}\theta +y\cos^{3}\theta=\sin\theta\cos\theta$ and $x\sin\theta-y\cos\theta=0$, then the value of $\left ( x^{2}+y^{2} \right )$ equals: